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the waves is ten centimeters per second. The speed of a wave, you conclude after thinking about it a moment, is the frequency times the wavelength.
    Bathtub waves and ocean waves are two-dimensional; they spread out from a point source as circles on the surface of the water. Sound waves, by contrast, are three-dimensional, spreading out in the air in all directions from the source of the sound. In the wave crest, the air is compressed a little; in the trough, the air is rarefied a little. Your ear detects these waves. The more often they come (the higher the frequency), the higher the pitch you hear.
    Musical tones are only a matter of how often the sound waves strike your ears. Middle C is how we describe 263 sound wavesreaching us every second; 263 hertz, it’s called. * What would be the wavelength of Middle C? If sound waves were directly visible, how far would it be from crest to crest? At sea level, sound travels at about 340 meters per second (about 700 miles per hour). Just as in the bathtub, the wavelength will be the speed of the wave divided by its frequency, or about 1.3 meters for Middle C—roughly, the height of a nine-year-old human.
    There is a class of puzzle thought to confound science—which goes something like, “What is Middle C to a person deaf from birth?” Well, it’s the same as it is to the rest of us: 263 hertz, a precise, unique frequency of sound belonging to this note and no other. If you can’t hear it directly, you can detect it unambiguously with an audio amplifier and an oscilloscope. Now of course this isn’t the same as experiencing the usual human perception of air waves—it utilizes sight rather than sound—but so what? All the information is there. You can sense chords and staccato, pizzicato, and timbre. You can associate with other times you’ve “heard” Middle C. Maybe the electronic representation of Middle C isn’t emotively the same as what a hearing person experiences, but even that may be a matter of experience. Even putting geniuses like Beethoven aside, you can be stone-deaf and experience music.

    This is also the solution to the old conundrum about whether, if a tree falls in the forest and there’s no one to hear, is a sound produced? Of course if we define a sound in terms of someone hearing it, by definition there was no sound. But this is an excessively anthropocentric definition. Clearly, if the tree falls, it makes sound waves, those sound waves can readily be detected by, say, a CD recorder, and when played back, the sound would be recognizably a tree falling in a forest. There is no mystery here.
    But the human ear is not a perfect detector of sound waves. There are frequencies (fewer than 20 waves arriving per second) that are too low for us to hear, although whales communicate readily in such low tones. Likewise, there are frequencies (more than 20,000 waves arriving every second) too high-pitched for adult humans to detect, although dogs have no difficulty (and respond when called at such frequencies by a whistle). Realms of sound exist—a million waves per second, say—that are, and always will be, unknown to direct human perception. Our sense organs, as superbly adapted as they are, have fundamental physical limitations.
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    It’s natural that we should communicate by sound. Our primate relatives certainly do. We’re gregarious and mutually interdependent—there’s a real necessity behind our communication talents.So, as our brains grew at an unprecedented rate over the last few million years, and as specialized regions of the cerebral cortex in charge of language evolved, our vocabulary proliferated. There was more and more that we were able to put into sounds.
    When we were hunter-gatherers, language became essential for planning the day’s activity, teaching the children, cementing friendships, alerting the others to danger, and sitting around the fire after dinner watching the stars come out and telling stories. Eventually, we invented